Proof of a conjecture of N. Konno for the 1D contact process

Consider the one-dimensional contact process. About ten years ago, N. Konno stated the conjecture that, for all positive integers $n,m$, the upper invariant measure has the following property: Conditioned on the event that $O$ is infected, the events $\{$All sites $-n,...,-1$ are healthy$\}$ and $\{$All sites $1,...,m$ are healthy$\}$ are negatively correlated. We prove (a stronger version of) this conjecture, and explain that in some sense it is a dual version of the planar case of one of our results in \citeBHK.Comment: Published at http://dx.doi.org/10.1214/074921706000000031 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Evaluation of the Swedish breeding program for cavalier King Charles spaniels

A breeding program with the aim of reducing the prevalence of mitral regurgitation (MR) caused by myxomatous mitral valve disease (MMVD) in Cavalier King Charles Spaniels (CKCS) is currently ongoing in Sweden. In this investigation 353 CKCS were selected as a sample of the population and 150 were examined by auscultation for heart murmurs when they reached the age of six years in 2007 and 2009. The aim with this investigation was to study the prevalence of heart murmurs in six-year-old CKCS and to estimate if prevalence has decreased since the breeding program was introduced 2001. The effect of the breeding program was evaluated by comparing the prevalence of heart murmurs in the two groups. In 2007, the prevalence of heart murmurs was 52% (50% for females and 54% for males) and in 2009, the prevalence was 55% (44% for females and 67% for males). No significant difference was found in the prevalence of heart murmurs between 2007 and 2009 (P = 0.8). For all six-year-old CKCS, the prevalence of heart murmur was 53% (females 46% and males 61%), which is higher than previous Swedish investigations

Some conditional correlation inequalities for percolation and related processes

Consider ordinary bond percolation on a finite or countably infinite graph. Let s, t, a and b be vertices. An earlier paper proved the (nonintuitive) result that, conditioned on the event that there is no open path from s to t, the two events ``there is an open path from s to a' and ``there is an open path from s to b' are positively correlated. In the present paper we further investigate and generalize the theorem of which this result was a consequence. This leads to results saying, informally, that, with the above conditioning, the open cluster of s is conditionally positively (self-)associated and that it is conditionally negatively correlated with the open cluster of t. We also present analogues of some of our results for (a) random-cluster measures, and (b) directed percolation and contact processes, and observe that the latter lead to improvements of some of the results in a paper of Belitsky, Ferrari, Konno and Liggett (1997

Change of Diurnal Heart Rate Patterns During Pregnancy and Lactation in Dogs (Canis familiaris)

Pregnancy and lactation involve great demands on the cardiovascular system. The purpose of this study was to investigate how the heart rate and diurnal heart rate pattern change when dogs become pregnant or lactate. Five clinically healthy female beagle dogs were mated, and delivered three to seven healthy puppies. The heart rate was investigated with 24-h ECG (Holter) once during anoestrus, at 3, 5, 7 and 9 weeks of pregnancy, and at week 4 postpartum (lactation). However, at 9 weeks, the ECG could not be recorded for the fully 24 h in 4 of 5 dogs, because labour started and the dogs then appeared disturbed by the recordings. The results at this date are not included in the statistical comparison. The heart rate increased progressively during pregnancy and was still elevated at 4 weeks of lactation. During late pregnancy the difference in heart rates between daytime and nighttime became smaller, but the heart rate was significantly higher in daytime in all periods. In conclusion, the increased heart rates during pregnancy and lactation reflect increased demands on the cardiovascular system and may be important to consider in clinical practice

Percolation in invariant Poisson graphs with i.i.d. degrees

Let each point of a homogeneous Poisson process in R^d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution mu on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution mu. Leaving aside degenerate cases, we prove that for any mu there exist schemes that give only finite components as well as schemes that give infinite components. For a particular matching scheme that is a natural extension of Gale-Shapley stable marriage, we give sufficient conditions on mu for the absence and presence of infinite components

Critical phenomena in exponential random graphs

The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence between particle states in a grand canonical ensemble of statistical physics. By adjusting the specific values of these subgraph densities, one can analyze the influence of various local features on the global structure of the network. Loosely put, a phase transition occurs when a singularity arises in the limiting free energy density, as it is the generating function for the limiting expectations of all thermodynamic observables. We derive the full phase diagram for a large family of 3-parameter exponential random graph models with attraction and show that they all consist of a first order surface phase transition bordered by a second order critical curve.Comment: 14 pages, 8 figure

Impact of blood tube additives and timing of sampling on blood taurine concentrations in clinically healthy dogs

Introduction: Dilated cardiomyopathy can be associated with taurine deficiency in dogs. Blood taurine concentrations can be analyzed in whole blood (WB) and plasma. The study objectives were to investigate agreement between taurine concentrations measured in WB, heparin plasma, and EDTA plasma, deter-mine intraindividual variation in healthy dogs, and evaluate if time from feeding to sampling impacts concentrations. Animals: 10 English Cocker spaniels and 10 dogs of various breeds. Materials and methods: Dogs were fasted 12 h prior to initial blood sampling, and the blood was collected at five occasions over 8 h. Food was offered immediately after first and 1 h after fourth sampling time point. Results: Agreement between taurine concentrations in EDTA plasma and hepari-nized plasma was good (mean difference 4.5 nmol/mL, 95% confidence interval (CI) 36.8-45.8 nmol/mL). WB concentrations were systematically higher than EDTA and heparin plasma concentrations (mean difference 132.7 nmol/mL, 95% CI 23.6-241.8 nmol/mL, and 127.6 nmol/mL, 95% CI 28.6-226.6 nmol/mL, respectively, all P < 0.001). Intraindividual daily variations in taurine concentration were seen in all additives, with largest variations in plasma (P < 0.001). Taurine concentration in heparinized plasma was higher at first and fifth sampling time points compared to the fourth (P 1/4 0.014). Discussion: Agreement was found between taurine concentrations measured in dif-ferent additives, with expected higher concentration in WB than plasma. Taurine concentrations measured in heparinized plasma varied with sampling time point. Intraindividual daily variations were observed in all additives, but mainly in plasma samples. Conclusion: Taurine concentrations in dogs with suspected deficiency should be in-terpreted with caution. 2022 The Authors. Published by Elsevier B.V